A Higher Probability of Detecting Lensed Supermassive Black Hole Binaries by LISA

Abstract

Gravitational lensing of gravitational waves (GWs) is a powerful probe of the matter distribution in the universe. Here we study the lensing effect induced by dark matter (DM) halos on the GW signals from merging massive black holes, and we revisit the possibility of detection using the Laser Interferometer Space Antenna (LISA). In particular, we include the halos in the low-mass range of 10 5 − 10 9 M since they are the most numerous according to the cold DM model. In addition, we employ the matched-filtering technique to search for weak diffraction signatures when the MBHBs have large impact parameters (y ∼ 10 2 ). We find that about (20 − 40)% of the MBHB in the mass range of 10 5 − 10 6 M and the redshift range of 4 − 10 should show detectable wave-optics effects. The uncertainty comes mainly from the mass function of DM halos. Not detecting any signal during the LISA mission would imply that DM halos are significantly more massive than 10 8 M .

Characteristic features of gravitational wave lensing as probe of lens mass model

“…Nonetheless, detection of lensed events is expected to happen in the near future [15][16][17][18][19][20]. In particular, [16] shows that strong lensing rate of GWs produced by elliptical galaxies is ≈ 0.2 yr −1 for LIGO and ≈ 1 yr −1 for aLIGO, and [17] adds that, for the nominal Einstein Telescope sensitivity, the rate of lensing events could rise to ∼ 80 yr −1 .…”

“…In [31] the authors use PM and SIS lenses and show that diffraction effects are important when we consider GWs in the LIGO frequency band lensed by objects with masses 100 M . Finally, [18] also considers small phase effects to recognize lensed signal, in this case for LISA sources, and with a large impact parameter, considering only SIS models. They find that, as already stated above, ∼ 1% of the sources should show detectable WO effects.…”

“…In [22], the authors claim that ∼ 0.1% of observed events are expected to be strongly lensed in the 3rd generation and a paolo.cremonese@usz.edu.pl b d.f.mota@astro.uio.no c vincenzo.salzano@usz.edu.pl that ET/CE will detect ∼ 50 lensed pairs per year. Regarding LISA mission [23], in its mass and lens range, [18] initially found that about 20 − 40% of the massive BBHs in the mass range of 10 5 − 10 6 M and the redshift range of 4 − 10 should show detectable wave-optics effects. However, the authors of [18] have revisited their analysis, considering more realistic scenarios, concluding that the resulted probability of detecting a lensed event in diffraction limit will not be as high as initially mentioned, but one order of magnitude smaller, i.e.…”

“…Regarding LISA mission [23], in its mass and lens range, [18] initially found that about 20 − 40% of the massive BBHs in the mass range of 10 5 − 10 6 M and the redshift range of 4 − 10 should show detectable wave-optics effects. However, the authors of [18] have revisited their analysis, considering more realistic scenarios, concluding that the resulted probability of detecting a lensed event in diffraction limit will not be as high as initially mentioned, but one order of magnitude smaller, i.e. ∼ 1% 1 .…”